quiz_1_2005 - Quiz #1 1.5 hours - open books and notes...

Quiz #1 1.5 hours - open books and notes Problem 1 (25 points) A device has a sensor connected to an alarming system. The sensor triggers with probability 0.95 if dangerous conditions exist in a given day and with probability 0.005 if conditions are normal during the day. Days with dangerous conditions occur with probability 0.005. Given the above: (a) What is the probability of false alarm, i.e. the probability that conditions are normal when the alarm system triggers? (b) What is the probability of unidentified critical condition, i.e. the probability that conditions are dangerous when the system does not trigger? (c) How many false alarms and how many unidentified critical conditions should be expected to occur during a 10-year period? Comment on the effectiveness of the alarming system. Problem 2 (25 points) At a given site, flood-producing storms occur with mean rate λ = 1/(20 years). (a) Considering the three conditions under which a point process is Poisson, state

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